NDLI: Ordinary differential equation for local accumulation time

Content Provider	PubMed Central
Author	Berezhkovskii, Alexander M.
Copyright Year	2011
Abstract	Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation.
Related Links	http://dx.doi.org/10.1063/1.3624898
Starting Page	74112
File Format	PDF
ISSN	00219606
e-ISSN	10897690
Journal	The Journal of Chemical Physics
Issue Number	7
Volume Number	135
Language	English
Publisher	U.S. Government
Publisher Date	2011-01-01
Access Restriction	Open
Rights Holder	U.S. Government
Subject Keyword	Physical and Theoretical Chemistry Physics and Astronomy(all) Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Medicine Physical and Theoretical Chemistry

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